SearchingSampling: Searching-Sampling

In RobustIV: Robust Instrumental Variable Methods in Linear Models

Searching-Sampling

Description

Construct Searching and Sampling confidence intervals for the causal effect, which provides the robust inference of the treatment effect in the presence of invalid instrumental variables in both low-dimensional and high-dimensional settings. It is robust to the mistakes in separating valid and invalid instruments.

Usage

SearchingSampling(
  Y,
  D,
  Z,
  X = NULL,
  intercept = TRUE,
  method = c("OLS", "DeLasso", "Fast.DeLasso"),
  robust = TRUE,
  Sampling = TRUE,
  alpha = 0.05,
  CI.init = NULL,
  a = 0.6,
  rho = NULL,
  M = 1000,
  prop = 0.1,
  filtering = TRUE,
  tuning.1st = NULL,
  tuning.2nd = NULL
)

Arguments

Y	The outcome observation, a vector of length n.
D	The treatment observation, a vector of length n.
Z	The instrument observation of dimension n \times p_z.
X	The covariates observation of dimension n \times p_x.
intercept	Whether the intercept is included. (default = TRUE)
method	The method used to estimate the reduced form parameters. "OLS" stands for ordinary least squares, "DeLasso" stands for the debiased Lasso estimator, and "Fast.DeLasso" stands for the debiased Lasso estimator with fast algorithm. (default = "OLS")
robust	If TRUE, the method is robust to heteroskedastic errors. If FALSE, the method assumes homoskedastic errors. (default = TRUE)
Sampling	If TRUE, use the proposed sampling method; else use the proposed searching method. (default=TRUE)
alpha	The significance level (default=0.05)
CI.init	An initial range for beta. If NULL, it will be generated automatically. (default=NULL)
a	The grid size for constructing beta grids. (default=0.6)
rho	The shrinkage parameter for the sampling method. (default=NULL)
M	The resampling size for the sampling method. (default = 1000)
prop	The proportion of non-empty intervals used for the sampling method. (default=0.1)
filtering	Filtering the resampled data or not. (default=TRUE)
tuning.1st	The tuning parameter used in the 1st stage to select relevant instruments. If NULL, it will be generated data-dependently, see Details. (default=NULL)
tuning.2nd	The tuning parameter used in the 2nd stage to select valid instruments. If NULL, it will be generated data-dependently, see Details. (default=NULL)

Details

When robust = TRUE, the method will be input as ’OLS’. For rho, M, prop, and filtering, they are required only for Sampling = TRUE. As for tuning parameter in the 1st stage and 2nd stage, if do not specify, for method "OLS" we adopt √{\log n} for both tuning parameters, and for other methods we adopt \max{(√{2.01 \log p_z}, √{\log n})} for both tuning parameters.

Value

SearchingSampling returns an object of class "SS", which is a list containing the following components:

ci	1-alpha confidence interval for beta.
SHat	The set of selected relevant IVs.
VHat	The initial set of selected relevant and valid IVs.
check	The indicator that the plurality rule is satisfied.

References

Guo, Z. (2021), Causal Inference with Invalid Instruments: Post-selection Problems and A Solution Using Searching and Sampling, Preprint arXiv:2104.06911.

Examples

data("lineardata")
Y <- lineardata[,"Y"]
D <- lineardata[,"D"]
Z <- as.matrix(lineardata[,c("Z.1","Z.2","Z.3","Z.4","Z.5","Z.6","Z.7","Z.8")])
X <- as.matrix(lineardata[,c("age","sex")])
Searching.model <- SearchingSampling(Y,D,Z,X, Sampling = FALSE)
summary(Searching.model)
Sampling.model <- SearchingSampling(Y,D,Z,X)
summary(Sampling.model)

RobustIV documentation built on Dec. 28, 2022, 1:42 a.m.